Decimal Place Value and Powers of Ten
Decimal place value and powers of ten covers understanding the value of each digit in a decimal number and multiplying or dividing by 10, 100 and 1000 by shifting the decimal point. This underpins almost every other decimal calculation on an 11+ paper, and it is tested on its own through quick-fire place-value and shifting questions that must be answered without a calculator.
Method
- Identify the place value of each digit in a decimal relative to the decimal point: tenths, hundredths, thousandths, counting to the right from the point.
- Remember that multiplying by 10 moves every digit one place to the left (making the number bigger), and dividing by 10 moves every digit one place to the right (making it smaller).
- For 100, shift two places; for 1000, shift three places, using the same direction rules as above.
- Keep the decimal point fixed in your mind and think of the digits moving through it, rather than randomly adding or removing zeros.
- When a shift takes a digit past the units column, insert a zero as a placeholder so the value stays correct.
- Check your answer's size makes sense: multiplying always makes a positive number bigger, and dividing always makes it smaller.
Worked example
Work out 0.47 x 1000 and 6.2 divided by 100.
- To multiply by 1000, move every digit three places to the left.
- 0.47 x 1000: the digits 4 and 7 shift three places left, giving 470.
- To divide by 100, move every digit two places to the right.
- 6.2 divided by 100: the digits 6 and 2 shift two places right, giving 0.062.
Practice questions
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Q1In the number 5.372, what is the value of the digit 7?Show answer
Answer: 0.07 (seven hundredths)
Q2Work out 3.6 x 10.Show answer
Answer: 36
Q3Work out 8.5 x 100.Show answer
Answer: 850
Q4Work out 91 divided by 1000.Show answer
Answer: 0.091
Q5Work out 0.026 x 100.Show answer
Answer: 2.6
Q6Find the value of 0.3 x 10 x 10.Show answer
Answer: 30 (0.3 x 10 = 3, then 3 x 10 = 30)
Q7Explain why dividing a number by 100 gives a smaller result than dividing the same number by 10.Show answer
Answer: Dividing by 100 shifts every digit two places to the right instead of one, which is a bigger reduction than dividing by 10, so the result is smaller; for example, 40 divided by 10 = 4, but 40 divided by 100 = 0.4.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Work out 0.049 x 100, showing your method.
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A single grain of rice has a mass of 0.029 grams. (a) Work out the mass, in grams, of 1000 grains of rice. (b) Work out the mass, in grams, of 10 grains of rice. (c) State, with a reason, which of your two answers is closer to the mass of a small paperclip, which has a mass of about 0.3 grams.
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Free printable worksheet
Want more practice on paper? Download the decimal place value and powers of ten 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 43 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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