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2D Understanding place value

Our number system is a base ten or decimal system – it works by using 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9). We use these ten digits to make up all our numbers. Each digit in a number is related to its next digit by being 10 times bigger or onetenth as big – the value goes up by 10 times as you go left (× 10) or down by 10 times as you go to the right (÷ 10).

Where the digit is, or its place in the number, tells us what the value of that digit actually is. This is called place value.

The first digit in a whole number (that’s the one just to the left of the decimal point) is worth 1 (sometimes we call it units).

The next one across on its left is worth 10 times more (× 10).

The next one across on its left is worth 10 times more again (× 100).

The next one across on its left is worth 10 time more again (×1000), and so on. We divide by 10 when we go across into the decimal fractions from the left to the right.

The first decimal place after the decimal point is therefore 1 divided by 10, which is tenths 1 10 th

.

Then the second decimal place is one-tenth as big again, which is hundredths

Consider the number 57.65. This number has a whole number part (before the decimal point) and a fraction part (after the decimal point).

When we say large numbers, it is helpful to think of them in groups of three.

With decimal numbers, we can say them in two ways.

1. As digits. e.g. 7.6 is seven point six 5.25 is five point two five

2. As fractions. 7.6 is seven and six tenths 5.25 is five and twenty-five hundredths.

2D Tasks and questions

Thinking task

1 Make up a very large number (excluding infinity!) and write it down. Read your number aloud.

Can you think of a shorthand way of writing your number?

Skills questions

2 Write the following numbers out as if you would say them. For example, 398 476 would be three hundred and ninety-eight thousand, four hundred and seventy-six.

3 Write the following decimals out as you would say them.

Mathematical literacy

4 Here is a place-value chart to help remind you of the place value for decimal numbers. Complete the table by writing in either the number in words or the missing digits. The first two are done for you.

1000s100s10s1s

145•7 one hundred and forty-five point seven

5782•61five thousand, seven hundred and eighty-two and sixty-one hundredths

• seven hundred and thirty-one point five eight

• seven thousand, four hundred and twenty-six and five tenths

• nine thousand and forty point eight seven

• two thousand, two hundred and twelve and five hundredths