There are some questions scattered about in the text below. Try and answer them without using a calculator.
Digits
There are ten decimal digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Examples: The number 2543 has four digits: 2, 5, 4 and
3.
The
number 145.09 has five digits: 1, 4, 5, 0 and 9.
What is a decimal number?
9876 ÷ 10 = 987.6 (there is one
digit after the decimal point and 10 has one nought).
23456 ÷ 100 = 234.56 (there are two
digits after the decimal point and 100 has two noughts).
13579 ÷ 1000 = 13.579 (there are three
digits after the decimal point and 1000 has three noughts).
864208 ÷ 10000 = 86.4208 (there are
four digits after the decimal point and 10000 has four
noughts).
etc
So if you count the number of digits after the decimal point, you know whether the same number without the decimal point has been divided by 10 or 100 or 1000 etc.
Note: 123.0 = 123.00 = 123.000 = 123 (trailing zeros don't count for
anything.)
Similarly, 357.900 = 357.90 = 357.9
Question: (a) What is 999 ÷ 100 ? (b) What is 98 ÷ 10000 ? (c) What is 4.567 x 100 ? (d) What is 1.2 x 100 ?
Converting a fraction to a decimal
The line between the top and bottom number in a fraction represents the operation ÷ (divide), so a fraction can be converted into a decimal by dividing the top number by the bottom number.
Example: 1/2 is the same as 1 ÷ 2 = 0.5
Question: convert 3/4 to a decimal.
Comparing Fractions and Decimals
The easiest way to compare a fraction to a decimal is to convert the fraction to a decimal.
Question: what is bigger: 2/3 ?
Adding and Subtracting Decimals
Write the numbers down, one underneath the other, keeping the decimal points in line and all the other numbers in the right 'place'.
Example: 2.345 - 0.05
| 2.345 0.05 |
| 2.295 |
Question: (a) What is the value of 666.71 - 33.7 ? (b) What is the value of 24.1 - 3.25?
Multiplying Decimals
What is the value of 54.321 x 0.06 ?
(a) Perform the multiplication as if there were no decimal points in it (i.e. 54321 x 6 = 325926)
(b) Count the total number of digits there are after the decimal points in both the original numbers (i.e. 3 + 2 = 5)
(c) Insert the decimal point so that this number (5) of digits fall after it (i.e. 3.25926)
(d) Do a rough estimate to check that your answer is about the right size.
Question: (a) What is the value of 23.01 x 2.2 ? What is the value of 0.002 x 3.3 ?
Dividing Decimals
Example: 315 ÷ 1.2
This is the same as 315/1.2
315/1.2 = 3150/12 (multiplying top and bottom by 10) = 262.5
(Remember: if you multiply the top of a fraction by a number and then multiply the bottom of the fraction by the same number, the fraction keeps the same value. )
Question: what are the values of (a) 26 ÷ 1.3 (b) 3.2 ÷ 0.16 (c) 0.8 ÷ 4 ?