Number, Place Value and Rounding

Where a digit sits decides its value

Two ideas run through all of number work: WHERE a digit sits decides how much it is worth, and ROUNDING lets you swap an awkward number for a sensible nearby one. ⭐⭐ PLACE VALUE: the same digit means different amounts depending on its column. In 3400 the 3 is worth three thousand; in 340 it is worth three hundred; in 3.4 it is worth three units. Read the columns and you read the number. ⭐ ROUNDING replaces a number with a nearby, tidier one. You can round to the nearest 10, 100 or 1000, or to a number of DECIMAL PLACES, or to a number of SIGNIFICANT FIGURES. The rule is the same each time: look at the next digit along, and if it is 5 or more, round up; if it is 4 or less, round down. ⭐⭐ ESTIMATING uses rounding on purpose: swap the numbers for easy ones, do the sum in your head, and get a rough answer to CHECK a real calculation. If your worked answer is far from your estimate, something has gone wrong. This module is place value, rounding and estimating. The other number topics each have their own module. ⚠️ Carry one question the whole way through: which place am I rounding to, and is the next digit 5 or more?

Three ways to round

The same rule, applied to three different targets. Read across each one.

Tap the two correct roundings

Tap the TWO statements where the number has been rounded correctly.

• 38 rounded to the nearest ten is 40.
• 4.62 rounded to one decimal place is 4.6.
• 3672 rounded to the nearest hundred is 3600.
• 4.62 rounded to one decimal place is 4.7.

Rounding to one decimal place

A scientist measures a mass as 6.749 grams and a results table asks for it to one decimal place. Which value should be written in the table?

• 6.7
• 6.8
• 6.75
• 7.0

The words number work uses

Six terms this topic turns on. Learn them and rounding reads clearly.

Pair each rounding with its result

Two true things about rounding

Select the TWO statements that are true.

• When the next digit is 5 or more, you round up
• In 3400 the digit 3 stands for three thousand
• Rounding always makes a number larger
• An estimate should be the exact answer to the calculation

Rounding without slips

Careful rounding is easy marks, and estimating is a free check on every calculation. ⭐⭐ DECIDE THE PLACE FIRST. Underline the digit in the place you are rounding to, whether that is the hundreds column or the first decimal place. Knowing exactly which digit you are keeping stops most mistakes. ⭐ LOOK AT ONE DIGIT ONLY. Check just the next digit along: 5 or more rounds up, 4 or less rounds down. Do not chain the rounding by looking further along, which is a common error. ⭐⭐ ESTIMATE TO CHECK. Round every number in a calculation to one easy figure, work it out in your head, and compare. If a worked answer is many times bigger or smaller than the estimate, a place-value slip has probably crept in. DO NOT DRIFT INTO OTHER NUMBER TOPICS. Fractions, percentages and indices each have their own module; here, keep the focus on place value, rounding and estimating. ⚠️ A note on care. Keep the trailing zeros that hold the place: 3672 to the nearest hundred is 3700, not 37, because the zeros keep the other digits in their columns. Keep the one question to hand: which place am I rounding to, and is the next digit 5 or more?

Order the steps to round a number

Put the steps for rounding a number to a chosen place into the right order.

• Find the digit in the place you are rounding to
• Look at the digit immediately to its right
• If it is 5 or more round up, if 4 or less round down
• Change the chosen digit up, or leave it, as decided
• Replace the digits after it with zeros or drop them

Round it yourself

Round 3672 to the nearest hundred. Type just the number.

The rounding run

Five quick decisions about place value and rounding. Three lives.

How long will it take

Leave the maths aside for a moment. Think about how you answer when somebody asks how long a journey will take. ⭐ If a friend casually asks over coffee, you say about half an hour. You do not say twenty-nine minutes and forty seconds; a tidy nearby figure is far more useful, and nobody wants the tiny detail. ⭐⭐ But if you are catching a train that leaves at a fixed minute, suddenly the tidy figure is not enough: now you care about the exact minutes, because being a little out means missing it. The SAME journey deserves a different amount of detail depending on WHY you are asking. So you are always making a quiet choice: how much detail is worth giving here? Too much and it is fussy and hard to use; too little and it is not accurate enough for the job. You pick a sensible level for the purpose, and you give a neat nearby value that is easy to hold in your head. ⚠️ Hold that picture. Working with numbers is the same: you choose a sensible level of detail for the job, and swap an awkward number for a tidy nearby one that is good enough for the purpose.

Finish each number line

The value a digit has because of its position is its _____ value. To replace a number with a sensible nearby value is to _____ it. A position after the point, such as the 7 in 3.7, is a _____ place. A digit that carries meaning, counted from the first non-zero digit, is a _____ figure. To find a rough answer by using easy numbers is to _____.

Three rounding decisions

Three real situations are described. For each, choose the sensible rounding decision.

• A minibus holds 15 people, and 47 people need transport. A student divides and gets 3.13 buses, then rounds to 3.
• A shopper wants to check quickly whether items priced 3.90, 5.10 and 1.95 come to about the right total at the till.
• A measurement is written as 2.5057 metres and a report asks for it to two decimal places.

Explain place value and rounding

Explain place value and rounding: what place value means, how to round a number to a chosen place using the next digit, and how estimating by rounding can check a calculation. Give a worked example of rounding and one of estimating.

• Explain what place value means, with an example
• Explain the rule for rounding using the next digit
• Give a worked example of rounding to a decimal place
• Explain how estimating by rounding checks a calculation
• Explain why trailing zeros must be kept when rounding whole numbers