दशमलव और रूपांतरण
Decimals and Conversion
A decimal is another way of writing a fraction whose denominator is 10, 100, 1000 and so on. The decimal point separates the whole from the part, and the places to its right are tenths, hundredths and thousandths — an extension of place value, not a new system.
Decimal place value
| Place | Value | In 45.678 |
|---|---|---|
| Tens | 10 | 4 |
| Ones | 1 | 5 |
| Tenths | 1/10 | 6 |
| Hundredths | 1/100 | 7 |
| Thousandths | 1/1000 | 8 |
So 45.678 is 45 + 6/10 + 7/100 + 8/1000. Adding zeros at the end of a decimal does not change its value: 0.5 = 0.50 = 0.500. Adding a zero before the digits does change it: 0.5 is not 0.05.
Converting between forms
- Fraction to decimal — divide numerator by denominator, or make the denominator 10, 100 or 1000. 3/4 = 75/100 = 0.75.
- Decimal to fraction — write the digits over the matching power of ten and simplify. 0.6 = 6/10 = 3/5.
- Decimal to percentage — multiply by 100. 0.35 becomes 35 per cent.
- Fraction to percentage — convert to a decimal, then multiply by 100. 1/8 = 0.125 = 12.5 per cent.
Operations with decimals
- Addition and subtraction: line up the decimal points, filling gaps with zeros.
- Multiplication: multiply as whole numbers, then place the point so that the answer has as many decimal places as the two numbers together. 1.2 x 0.3 = 0.36.
- Division: shift the point in both numbers until the divisor is a whole number, then divide as usual.
Money, measurement and decimals
Decimals enter a primary child's life first through money and measurement, and this is the right entry point. Rupees and paise are hundredths, so 12 rupees 50 paise is 12.50. A length of 1 metre 25 centimetres is 1.25 metres, and a weight of 2 kilograms 500 grams is 2.5 kilograms. Working with real bills and a measuring tape builds decimal place value far more securely than a page of conversions.
Comparing decimals
Compare whole-number parts first, then tenths, then hundredths. A common error is judging by length: children read 0.125 as larger than 0.4 because it has more digits. Writing 0.4 as 0.400 settles it instantly.
✗ 0.125 is greater than 0.4 because it has more digits. | ✓ 0.4 = 0.400 is greater than 0.125; compare place by place.
संकेत: दशमलव के बाद पहला स्थान दशांश, दूसरा शतांश, तीसरा सहस्रांश; अंत में शून्य जोड़ने से मान नहीं बदलता।
Decimals give one or two questions, usually a conversion or a comparison. The most repeated trap is the length misconception above, which is also asked as a pedagogy item about what a child has misunderstood. In multiplication questions, count the decimal places carefully — this is the error most candidates make under time pressure. Keep the common conversions ready: 1/2 = 0.5 = 50 per cent, 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125, 3/4 = 0.75.
Frequently asked questions
How do you convert a fraction into a decimal?
Divide the numerator by the denominator, or convert the fraction so that its denominator becomes 10, 100 or 1000 and then read off the digits. For example, three-quarters becomes 75 over 100, which is 0.75.
Does adding a zero change the value of a decimal?
Adding a zero at the right-hand end does not change the value, so 0.5 equals 0.50. Adding a zero immediately after the decimal point does change it, since 0.05 is one tenth of 0.5.
Which is greater, 0.4 or 0.125?
0.4 is greater. Comparing decimals is done place by place, not by counting digits. Writing 0.4 as 0.400 makes the comparison with 0.125 immediately clear.
60-second recap
- Decimal places are tenths, hundredths, thousandths — an extension of place value.
- Trailing zeros do not change a decimal's value; leading zeros after the point do.
- Fraction to decimal: divide, or make the denominator a power of ten.
- In multiplication, total decimal places in the answer equal the sum of the two.
- Compare place by place, never by the number of digits.