Place Value, Ordering and Rounding
Place value is the idea that a digit's worth depends on its position in a number: in 4725 the digit 7 is worth 700 because it sits in the hundreds column, but in 4.725 the same digit 7 is worth 0.7 because it sits in the tenths column. Ordering numbers by size, from smallest to largest or the reverse, means comparing decimals digit by digit from the biggest place value column downwards, rather than by how many digits are written.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Identify the value of each digit in a number by its position (column) relative to the decimal point: thousands, hundreds, tens, units, tenths, hundredths, thousandths.
- To compare two numbers, look at the digits in the highest place value column first; the number with the bigger digit there is bigger, regardless of how many digits are written after it.
- To order decimals safely, write every number to the same number of decimal places by adding trailing zeros, then compare column by column from the tenths place onwards; remove the padding zeros again when you state the final order.
- Remember that any negative number is smaller than any positive number, and zero sits between them; among negative numbers, the one nearer to zero is the larger value.
- To round to a given place value, find the digit in that column, then look only at the very next digit to its right: 5 or more rounds up, below 5 leaves it unchanged.
- Once you have rounded, replace every digit to the right of the rounded place with a zero (for a whole number) or remove it entirely (for a decimal).
- Watch for numbers that round up through a 9, such as rounding 6.995 to 1 decimal place, where the 9 rounds up and carries into the units digit.
Worked example
In a school sports day, five runners' times for the 100 m race were recorded in seconds: 12.84, 12.4, 12.809, 12.48, 12.09. (a) Write the five times in order, starting with the fastest (smallest) time. (b) Round the fastest time to 1 decimal place.
- Write every time to three decimal places by adding trailing zeros so the columns line up: 12.840, 12.400, 12.809, 12.480, 12.090.
- Compare the tenths digit of each: 12.090 has tenths digit 0, which is the smallest of the five, so this is the fastest time.
- Of the remaining times, 12.400 and 12.480 both have tenths digit 4, while 12.840 and 12.809 both have tenths digit 8, so compare their hundredths digits next: 12.400 (hundredths 0) is smaller than 12.480 (hundredths 8), and 12.809 (hundredths 0) is smaller than 12.840 (hundredths 4).
- Putting the five times in order of size gives the fastest to slowest order: 12.09, 12.4, 12.48, 12.809, 12.84 seconds.
- To round the fastest time, 12.09, to 1 decimal place, look at the hundredths digit (9); since 9 is 5 or more, round the tenths digit up from 0 to 1, giving 12.1 seconds.
Practice questions
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Q1The number of spectators at a rugby match was 52914. Write down the value represented by the digit 9 in this number.Show answer
Answer: 900 (the digit 9 is in the hundreds column)
Q2Write down the value represented by the digit 3 in the number 47.038.Show answer
Answer: 0.03 (three hundredths, since the digit 3 is in the hundredths column)
Q3Write these javelin throw distances in order, starting with the longest: 41.6 m, 41.09 m, 41.65 m, 41.099 m, 41.9 m.Show answer
Answer: 41.9 m, 41.65 m, 41.6 m, 41.099 m, 41.09 m
Q4In a golf tournament, five players' scores relative to par were: -3, 5, -8, 0, -1. Write these scores in order from lowest (best) to highest.Show answer
Answer: -8, -3, -1, 0, 5
Q5Round 386540 to the nearest 10000.Show answer
Answer: 390000
Q6Round 7.0653 to 2 decimal places.Show answer
Answer: 7.07
Q7Write down the number that is exactly halfway between 5.3 and 5.4.Show answer
Answer: 5.35
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
The masses of five parcels, in kg, are 3.45, 3.4, 3.099, 3.09, 3.463. (a) Write the masses in order, starting with the lightest. (b) The heaviest parcel's mass is rounded to 1 decimal place for a shipping label. Write down this rounded mass.
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Priya rounds the number 6.995 to 1 decimal place and gets the answer 6.9. Explain the mistake Priya has made, and write down the correct answer.
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Using each of the digits 3, 0, 7 and 1 exactly once, write down (a) the largest possible 4-digit number, (b) the smallest possible 4-digit number that does not start with 0, (c) the difference between your two answers.
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Free printable worksheet
Want more practice on paper? Download the place value, ordering and rounding worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 4 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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