Decimal means 10. Decimal System is the numbering system used by humans, which is based on 10 digits.
Decimal System lets us write numbers as large or as small as we want, using the decimal point. Numbers can be placed to the left or right of a decimal point, to indicate values greater than one or less than one.
The number to the left of the decimal point is a whole number. |
The first digit on the right means tenths (1/10) |
As we move further right, every number place gets 10 times smaller (one tenth as big) |
As we move left, every number place gets 10 times bigger . |
Example: What is 2.3 ?
- On the left side is "2", that is the whole number part.
- The 3 is in the "tenths" position, meaning "3 tenths", or 3/10
- So, 2.3 is "2 and 3 tenths"
A decimal fraction is a fraction where the denominator is a power of ten.
Converting Fractions to Decimals
The simplest method is to use a calculator.
Just divide the top of the fraction by the bottom, and read off the answer ! | |
Example: What is ^{5}/_{8} as a fraction? | |
... get your calculator and type in "5 / 8 =", the answer should be 0.625 |
To convert a Fraction to a Decimal manually, follow these steps:
Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s. |
Step 2: Multiply both top and bottom by that number. |
Step 3. Then write down just the top number, putting the decimal place in the correct spot (one space from the right for every zero in the bottom number) |
For example: To express 3/4 as a Decimal, the steps are :
Step 1: Multiply 4 by 25 to make 100
Step 2: Multiply top and bottom by 25:
×25 | ||
3 | = | 75 |
4 | 100 | |
×25 |
Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros);
Answer = 0.75
Another example:
Expressing 1/3 as a Decimal :
Step 1: There is no way to multiply 3 to become 10 or 100 or any power of 10, but we can calculate an approximate decimal by choosing to multiply by, say, 333
Step 2: Multiply top and bottom by 333:
×333 | ||
1 | = | 333 |
3 | 999 | |
×333 |
Step 3: Now, 999 is nearly 1,000, so let us write down 333 with the decimal place 3 spaces from the right (because 1,000 has 3 zeros):
Answer = 0.333 (accurate to only 3 decimal places !!)
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decimals.