Accuracy, Approximation & Prepositions

3.6. Accuracy, Approximation & Prepositions

Why Approximation Matters

Charts and graphs in IELTS Task 1 rarely show exact round numbers. A bar might end somewhere between the gridlines. A line might peak at what looks like 78 or maybe 82 — you cannot be certain it is exactly 80.

This creates a problem. If you write "the figure was exactly 80 thousand" and the real value is 78,400, your report is inaccurate. The examiner knows the data, and they know you are guessing at precision you do not have.

The solution is approximation language. Instead of claiming false precision, you signal that you are giving a reasonable estimate:

Instead of thisWrite this
"The figure was 80 thousand.""The figure was approximately 80 thousand."
"Sales reached 3.5 million.""Sales reached just over 3 million."
"The number fell to 20%.""The number fell to nearly 20%."

Tip: Using approximation language actually helps your score. It demonstrates lexical range and shows the examiner that you understand how to report data responsibly — exactly what a well-trained academic writer does.

There are two situations where approximation language is essential:

  1. When you cannot read the exact value from the chart. Gridlines are spaced apart, and many values fall between them. Approximation is the honest way to report these figures.
  2. When you want to make a general comparison. Saying "roughly twice as many" is more effective than trying to calculate the precise ratio from estimated values.

And one situation where you should not use it: when the chart states an exact figure in a table cell or data label. If the number is printed clearly, report it directly.

Approximation Vocabulary

English has a rich set of expressions for indicating that a figure is not exact. You need to know several so that you can vary your language throughout a report.

Core Expressions

ExpressionMeaningExample
approximatelyaround a given number"approximately 45 thousand"
aboutaround a given number (slightly less formal)"about 3 million"
aroundnear a given number"around 65%"
roughlynear a given number (emphasises imprecision)"roughly half of all respondents"
just overslightly more than"just over 20 thousand"
just underslightly less than"just under 50%"
nearlyslightly less than (approaching from below)"nearly 4 million"
almostvery close to but not quite reaching"almost 90%"
close tonear a given number"close to 10 thousand"
in the region ofsomewhere near (wider range implied)"in the region of 2 million"
slightly more thana little above"slightly more than a third"
slightly less thana little below"slightly less than half"

Matching Exercise

Match each approximation expression (1-6) to its closest meaning (a-f).

#ExpressionMeaning
1just overa. around / near
2approximatelyb. slightly less than
3just underc. near but not reaching
4in the region ofd. slightly more than
5nearlye. somewhere near (broad estimate)
6roughlyf. near (emphasising imprecision)

Answers

1 — d2 — a3 — b4 — e5 — c6 — f

Tip: "Just over" and "just under" are among the most useful expressions in Task 1. They let you report a value that sits slightly above or below a gridline — which happens constantly in real IELTS charts.

Fractions as Verbs: Describing Proportional Change

When the data shows that something doubled, tripled, or halved, saying so is far more effective than listing two numbers and leaving the reader to do the maths. Fractions used as verbs are powerful summarising tools.

Key Fraction Vocabulary

ExpressionMeaningExample
doubledincreased to twice the original"Sales doubled between 2000 and 2010."
tripledincreased to three times the original"The population tripled over the period."
halveddecreased to half the original"Exports approximately halved."
rose by a quarterincreased by 25% of the original"Spending rose by roughly a quarter."
fell by a thirddecreased by about 33% of the original"Output fell by just over a third."
increased by (approximately) halfincreased by 50% of the original"Revenue increased by approximately half."

Notice how naturally these combine with approximation language: "approximately doubled," "rose by just over a quarter," "fell by nearly a third." This combination of fraction verbs and approximation expressions produces sentences that are both precise and sophisticated.

Practice: Electronic Goods Imports

<!-- Diagram note: The bar chart described below shows "Imports of electronic goods (millions of units)" for five product categories: DVD players, CD players, Televisions, Radios, and Video recorders. There are two bars per category — one for the year 2000 (light) and one for 2006 (dark). The y-axis runs from 0 to 10 million units. Approximate values — DVD players: 2000 (3.0m), 2006 (5.8m). CD players: 2000 (2.1m), 2006 (1.7m). Televisions: 2000 (6.2m), 2006 (8.5m). Radios: 2000 (4.0m), 2006 (5.2m). Video recorders: 2000 (6.2m), 2006 (2.8m). -->

Look at the bar chart described above: "Imports of electronic goods (millions of units)" comparing figures for 2000 and 2006 across five categories. Using the data below, write a sentence for each product that uses fraction vocabulary combined with approximation language.

Product20002006Change
DVD players3.0m5.8m+2.8m
CD players2.1m1.7m-0.4m
Televisions6.2m8.5m+2.3m
Radios4.0m5.2m+1.2m
Video recorders6.2m2.8m-3.4m

Try writing your sentences before looking at the suggested answers below.

1. DVD players (3.0m to 5.8m)

Think: 5.8 is close to 6.0, and 6.0 is double 3.0. So the figure nearly doubled, or approximately doubled.

Suggested answer: "Imports of DVD players nearly doubled / approximately doubled, rising from 3 million to just under 6 million units."

2. CD players (2.1m to 1.7m)

Think: The drop is 0.4m out of 2.1m. A quarter of 2.1 is about 0.525. The actual drop (0.4) is slightly less than a quarter. So the figure fell by just under a quarter or approximately a quarter.

Suggested answer: "CD player imports fell by just under a quarter / approximately a quarter, from 2.1 million to 1.7 million units."

3. Televisions (6.2m to 8.5m)

Think: The increase is 2.3m. A third of 6.2 is about 2.07. The actual rise (2.3) is slightly more than a third.

Suggested answer: "Television imports rose by just over a third / slightly more than a third, increasing from 6.2 million to 8.5 million."

4. Radios (4.0m to 5.2m)

Think: The increase is 1.2m. A quarter of 4.0 is 1.0. The actual rise (1.2) is slightly more than a quarter.

Suggested answer: "Imports of radios rose by slightly more than a quarter / just over a quarter, from 4 million to 5.2 million units."

5. Video recorders (6.2m to 2.8m)

Think: Half of 6.2 is 3.1. The figure dropped to 2.8, which is close to 3.1. So the figure approximately halved.

Suggested answer: "Video recorder imports approximately halved, declining from 6.2 million to 2.8 million units."

Tip: Fraction verbs let you summarise a change in a single powerful word. Instead of writing "the number went from 3 million to 5.8 million, which is an increase of 2.8 million," you can write "the number approximately doubled." The examiner rewards this kind of concise, analytical writing.

Prepositions of Time

Getting prepositions right is essential for accurate data reporting. A wrong preposition can change the meaning of your entire sentence. Here is a comprehensive reference.

PrepositionUseExample
inA month, year, decade, or named periodin January; in 2005; in the 1990s
atA specific point in time or positionat 9 o'clock; at the start of the period
from...toA range between two endpointsfrom 1990 to 2004
between...andA range between two endpointsbetween 1990 and 2004
duringThroughout or within a periodduring the recession; during the first decade
beforePrior to a point or periodbefore 2005; before the war
afterFollowing a point or periodafter the recession; after 1998
byAt some point before (and including) a deadlineby 2005 (= at some point before or at 2005)
untilContinuing up to a point in timeuntil March; until the end of the period
sinceFrom a past point continuing to nowsince the new laws were introduced

Tip: "From...to" and "between...and" are interchangeable in most Task 1 contexts, but never mix them: "from 1990 and 2004" and "between 1990 to 2004" are both incorrect.

Practice: Fill in the Preposition

Complete each sentence with the correct preposition(s) of time. Choose from: in, at, from...to, between...and, during, before, after, by, until, since.

#Sentence
1The number of tourists increased sharply ______ 2003 ______ 2008.
2Unemployment peaked ______ the start of the recession.
3______ 2010, the government had already introduced new policies.
4Sales remained stable ______ the first quarter of the year.
5The figure did not change significantly ______ March.
6______ the reforms were introduced, the trend reversed.
7There was a sharp decline ______ 1998 ______ 2002.
8______ the new tax laws were passed, revenue has increased steadily.
9The highest point was reached ______ 2007.

Answers

#AnswerExplanation
1from 2003 to 2008A range between two time points. "Between 2003 and 2008" is also correct.
2at the start of the recessionA specific point in time (the start).
3By 2010Meaning "at some point before 2010" — the policies were already in place.
4during the first quarterThroughout a period of time.
5until MarchThe figure stayed the same up to that point.
6After the reforms were introducedFollowing an event.
7between 1998 and 2002A range between two time points. "From 1998 to 2002" is also correct.
8Since the new tax laws were passedFrom a past event continuing to now (present perfect follows: "has increased").
9in 2007A specific year.

The Critical Difference: "by" vs "to" with Numbers

This is one of the most important distinctions in Task 1 writing. Confusing "by" and "to" with numbers does not just sound awkward — it reports completely different data.

"Rose BY 20,000" — the SIZE of the increase

"By" tells you how much something changed. It describes the gap between the old value and the new value.

"The population rose by 20,000."

This means: if the population was 40,000, it increased by 20,000, so it is now 60,000.

"Rose TO 20,000" — the POINT REACHED

"To" tells you where the value ended up. It describes the destination, not the journey.

"The population rose to 20,000."

This means: whatever the population was before (perhaps 5,000 or 12,000), it is now 20,000.

Side-by-Side Comparison

SentenceStarting valueChangeEnd value
"Sales rose by 20,000 to 60,000."40,000+20,00060,000
"Sales rose to 20,000."Unknown (but less than 20,000)Unknown20,000
"Sales fell by 10,000."Unknown-10,000Unknown
"Sales fell to 10,000."Unknown (but more than 10,000)Unknown10,000
"Sales rose by 10,000 to 50,000."40,000+10,00050,000

Tip: The most complete way to report a change is to use both: "The figure rose by 15,000 to reach 45,000." This tells the reader both the size of the change and the final value. However, you do not always need both — choose whichever is most relevant to the point you are making.

Getting this wrong is not a minor grammar error. If the figure rose from 40,000 to 60,000 and you write "rose to 20,000," you have reported entirely wrong data. The examiner will penalise this under Task Achievement, not just Grammatical Range.

Verbs and Their Prepositions

Different verbs follow different preposition patterns. Some require prepositions; others do not. Getting these patterns right is essential for accurate, natural-sounding reports.

Verbs That Take "to" or "by"

These verbs describe directional change and combine with to (destination) or by (amount of change):

Verb+ to (destination)+ by (amount)
riserose to 50,000rose by 10,000
increaseincreased to 3 millionincreased by 15%
fallfell to 20,000fell by a third
dropdropped to 8%dropped by 2 percentage points
declinedeclined to its lowest pointdeclined by 500 units
shoot upshot up to 90,000shot up by 40,000
plungeplunged to an all-time lowplunged by nearly half

Verbs That Take Other Prepositions

VerbPrepositionExample
stayatstayed at 25,000
remainatremained at approximately 10%
peakatpeaked at just over 60,000
fluctuatebetween...and / aroundfluctuated between 20 and 30 thousand; fluctuated around the 25,000 mark
level offatlevelled off at around 45%
stabiliseatstabilised at roughly 3 million

Verbs Without Prepositions

These verbs take a direct object — no preposition is needed:

VerbExample
reachreached 50,000 (NOT "reached to 50,000")
doubledoubled (or: doubled its value)
tripletripled over the period
halvehalved between 2000 and 2006
exceedexceeded 1 million for the first time
hithit a peak of 70,000

Tip: A common error is writing "reached to" — this is always wrong. "Reach" already means "arrive at," so adding "to" is redundant.

Nouns and Their Prepositions

When you use the noun form of a change verb, the preposition pattern shifts:

Noun+ of (amount)+ in (what changed)
a risea rise of 20%a rise in temperatures
an increasean increase of 5,000an increase in spending
a falla fall of 15%a fall in house prices
a decreasea decrease of 3 milliona decrease in the birth rate
a dropa drop of 10 percentage pointsa drop in attendance
a declinea decline of roughly a quartera decline in manufacturing output

Notice the pattern:

  • of answers "how much?"
  • in answers "in what?"

You can combine them: "There was a rise of approximately 20% in household energy consumption."

Tense Selection for Different Data Types

The time reference in the data determines which tense you should use. Getting the tense wrong signals to the examiner that you do not understand how English tenses relate to time — a serious issue for Grammatical Range and Accuracy.

Reference Table

Data typeTenseSignal wordsExample
Past data (completed period)Past simplein 2005, from 1990 to 2000, last year"In 2005, prices fell sharply."
By a specific past pointPast perfectby 2005, by the end of the decade"By 2005, prices had fallen to their lowest level."
From a past point to nowPresent perfectsince 2005, over the last decade"Since 2005, prices have fallen steadily."
Ongoing action from past to nowPresent perfect continuoussince, for the past decade"Prices have been falling since 2005."
Future prediction or projectionFuture / Future perfectby 2030, in the next decade, is expected to"By 2030, prices will have fallen by 20%."

When to Use Each Tense

Past simple is your default tense for most Task 1 data, because most charts show completed past periods (e.g., 1990-2010). Use it for stating what happened at a specific past time.

Past perfect is useful when you need to show that something was already true before another past event. "By 2005" implies "at some point before 2005, this had already happened."

Present perfect appears when the data runs up to the present. If the chart covers 2000 to now, you might write: "Since 2000, the figure has risen from 3 million to 8 million."

Present perfect continuous emphasises that a trend is still ongoing. "Prices have been rising since 2015" suggests the rise has not stopped.

Future forms appear when the chart includes projections. Words like "projected," "estimated," or "forecast" on the chart signal that you should use future tenses for those data points.

Practice: Choose the Correct Tense

Select the correct verb form for each sentence.

#SentenceOptions
1In 1998, the number of visitors ______ dramatically.a) has fallen b) fell c) had fallen
2Since the introduction of the new policy, unemployment ______ steadily.a) decreased b) has decreased c) had decreased
3By the end of 2010, the company ______ over 50,000 units.a) sold b) has sold c) had sold
4Passenger numbers ______ continuously since the airport opened in 2015.a) have been rising b) rose c) had risen
5According to the projections, energy consumption ______ by 30% by 2040.a) rose b) has risen c) will have risen

Answers

#AnswerExplanation
1b) fell"In 1998" specifies a completed past time. Past simple is correct.
2b) has decreased"Since the introduction" connects a past event to the present. Present perfect is correct.
3c) had sold"By the end of 2010" refers to a point before which the action was completed. Past perfect is correct.
4a) have been rising"Continuously since 2015" emphasises an ongoing action from past to present. Present perfect continuous is correct.
5c) will have risen"By 2040" is a future point by which the action will be completed. Future perfect is correct.

Worked Example: Crude Oil Prices (1970-2005)

<!-- Diagram note: The line graph described below shows "Crude oil prices per barrel (US dollars), 1970-2005." The x-axis shows years from 1970 to 2005. The y-axis shows price in US dollars per barrel (0-70). The line begins at approximately $2 in 1970 and remains low until 1973. Key events are annotated on the graph: "Arab oil embargo" at 1973 (price jumps to ~$12), "Iranian revolution" at 1979 (price rises sharply to ~$35), "Iran-Iraq war" at 1980 (price peaks at ~$40), then a gradual decline through the 1980s to ~$15 by 1986, some fluctuation around $15-20 through the late 1980s, a brief spike to ~$28 at "Invasion of Kuwait" in 1990, falling back to ~$15 by 1994, gradual rise to ~$25 by 2000, a dip to ~$20 in 2001, then a steep rise from 2002 with "Second Gulf crisis" annotated at 2003, reaching approximately $55-60 by 2005. -->

Read the description of the line graph above: "Crude oil prices per barrel (US dollars), 1970-2005." The graph tracks the price of crude oil over 35 years, with several geopolitical events annotated: the Arab oil embargo (1973), the Iranian revolution (1979), the Iran-Iraq war (1980), the invasion of Kuwait (1990), and the second Gulf crisis (2003).

Gap-Fill: Prepositions

Complete the paragraph below by filling in the correct prepositions. Choose from: in, at, from, to, by, between, and, during, after, until.

"______ (1) 1970, the price of crude oil was ______ (2) approximately $2 per barrel and remained low ______ (3) 1973. ______ (4) the Arab oil embargo, the price rose sharply ______ (5) around $12 — an increase ______ (6) roughly $10 ______ (7) just three years. The price continued to climb ______ (8) 1973 ______ (9) 1980, driven ______ (10) the Iranian revolution and the Iran-Iraq war, peaking ______ (11) approximately $40 per barrel.

______ (12) the early 1980s, prices fell steadily, dropping ______ (13) about $15 ______ (14) 1986. The price fluctuated ______ (15) $15 ______ (16) $20 ______ (17) 1993, apart from a brief spike ______ (18) the invasion of Kuwait ______ (19) 1990, when oil shot up ______ (20) around $28 ______ (21) falling back again.

______ (22) 2002, prices began rising steeply once more. ______ (23) the second Gulf crisis ______ (24) 2003, the price accelerated, and ______ (25) 2005, crude oil had reached ______ (26) the region of $55-60 per barrel — the highest level ______ (27) the entire 35-year period."

Answers

#Answer#Answer#Answer
1In10by19in
2at11at20to
3until12During / In21before
4During / After13to22From / After
5to14by23During / After
6of15between24in
7in16and25by
8from17until26in
9to18during27in / of

Tip: Notice how the worked example uses nearly every preposition from the reference table. In a real exam, your report will naturally require a similar range. If you find yourself using the same preposition repeatedly, it is a sign that you may be structuring your sentences too similarly — vary your constructions to demonstrate grammatical range.

Practice Exercises

Exercise 1: Approximation Rewrite

The sentences below use false precision. Rewrite each one using appropriate approximation language.

#Original sentenceRewrite using approximation
1The figure was 47,000 in 2005.
2Exports increased to 8.3 million tonnes.
3The percentage fell from 62% to 31%.
4Three times as many people used the service in 2010.
5There was a 25% rise in passenger numbers.

Suggested Answers

#Suggested rewrite
1The figure was approximately 47,000 / close to 47,000 in 2005.
2Exports increased to just over 8 million tonnes / roughly 8.3 million tonnes.
3The percentage approximately halved, falling from around 62% to just over 30%.
4The number of users roughly tripled / approximately tripled by 2010.
5There was a rise of approximately a quarter / roughly 25% in passenger numbers.

Exercise 2: "By" vs "To" — Which Is Correct?

Choose the correct preposition for each sentence, or write both if the sentence uses both.

#SentenceAnswer
1The number of students rose ______ 15,000 ______ reach 45,000.by ... to
2Unemployment fell ______ 3.2%.to (it reached 3.2%)
3Spending increased ______ approximately a third.by (the size of the increase was a third)
4House prices dropped ______ $50,000 ______ just $180,000.by ... to
5The figure climbed ______ its peak of 90,000.to (destination/point reached)

Exercise 3: Comprehensive Gap-Fill

Complete each sentence with the correct preposition and verb form.

#Sentence
1The number of visitors ______ (rise) ______ approximately 20% ______ 2005 ______ 2010.
2______ 2015, the government ______ (already / introduce) new regulations.
3Household spending ______ (increase) steadily ______ the new tax was implemented.
4The price peaked ______ just over $60 ______ July 2008.
5______ the 1990s, production ______ (fluctuate) ______ 20 ______ 30 thousand units.

Answers

#Answer
1The number of visitors rose by approximately 20% from 2005 to 2010.
2By 2015, the government had already introduced new regulations.
3Household spending has increased steadily since the new tax was implemented.
4The price peaked at just over $60 in July 2008.
5During the 1990s, production fluctuated between 20 and 30 thousand units.

Key Takeaways

  • Use approximation language whenever you cannot read an exact value from the chart. Writing "approximately," "just over," or "nearly" shows sophistication, not uncertainty.
  • Fraction verbs (doubled, tripled, halved, rose by a quarter) let you summarise proportional change concisely. Combine them with approximation expressions for maximum effect.
  • "By" and "to" with numbers mean completely different things. "Rose by 20,000" describes the size of the change; "rose to 20,000" describes the point reached. Confusing them reports wrong data.
  • Prepositions of time must be precise. "In 2005," "by 2005," "since 2005," and "until 2005" all mean different things.
  • Verbs have fixed preposition patterns. Rise/fall/increase take "to" or "by." Stay/remain/peak take "at." Reach and double take no preposition.
  • Tense follows time reference. Past simple for completed periods, present perfect for past-to-now, past perfect for "by + past point," and future forms for projections. Let the time phrase guide your choice.
  • Combine these skills for maximum impact: "By 2005, crude oil prices had risen to approximately $60 per barrel — roughly a tenfold increase from their 1970 level." One sentence, using tense, prepositions, approximation, and fraction language together.