Year 7. Decimals

Another way of writing the fraction 1/10 is as the decimal 0.1. Also 2/10 is 0.2 etc. If a fraction has 10 as its denominator, it is easy to write it in decimal form. We can practice this in a short exercise:

Exercise 1D

Number lines are often helpful in mathematics. In a number line we break the line up into equal sized smaller steps, to represent the numbers in-between two other numbers. Let’s practice drawing some below and using them to represent decimal number:

Exercise 1E & 1G

If the first digit after the decimal point represents tenths, then what does the second digit after the decimal point represent? So in a decimal number like 0.37 we have 3 tenths and 7 hundredths (we could also call this 37 hundredths). Let’s have a go at marking some decimals including hundredths on the number line.

Exercise 1H

Knowing the place value of each of the digits in a number helps us to order the numbers, because we know that a 1 in the “tenths” position is a lot larger than an 8 in the “thousandths” position.

Exercise 1I

When we deal with currency (i.e. money) the situation is a bit special. We have to know how many parts each unit of currency can be broken down into in order to write it correctly. In British currency, there is 100 pence in every pound, and if we want to say 12 pounds and 15 pence, we write it as £12.15. We never use more than two decimal places to refer to currency. US currency is very similar, as you will see in the exercise below.

Exercise 1J

Our number system is set up so that multiplying or dividing by numbers like 10, 100, 1000 is very easy. We should think of the decimal point as being fixed and all of the other numbers moving around it to do these calculations. We NEVER think about moving the decimal point. Sometimes we need to use zero digits to fill in missing spaces in our answer. Let’s try multiplying and dividing a few different numbers by 10, 100 or 1000 to see how this works in practice.

Exercise 1K

Exercise 1L


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