Decimals
Overview
Decimals are a way of writing numbers that are not whole numbers. They use a dot called the decimal point to separate the whole part from the fractional part. For example, 3.5 means 3 whole and 5 tenths. Decimals are used in everyday life for money, measurement, and weight. In this chapter, we learn to read, write, compare, and add or subtract decimal numbers easily.
Typed Notes
Understanding Decimal Place Values
Every digit in a decimal number has a place value. To the left of the decimal point we have ones, tens, hundreds and so on. To the right we have tenths (1/10), hundredths (1/100), and thousandths (1/1000). For example, in 4.37, the digit 4 is in the ones place, 3 is in the tenths place, and 7 is in the hundredths place. We read 4.37 as 'four point three seven'. Understanding place value helps us write, compare, and calculate with decimals correctly.
Converting Fractions to Decimals and Vice Versa
Fractions with denominators 10, 100, or 1000 can be easily written as decimals. For example, 7/10 = 0.7, 25/100 = 0.25, and 135/1000 = 0.135. Similarly, 0.6 means 6/10, and 0.08 means 8/100. We can also convert decimals back to fractions by reading the place value of the last digit. For example, 0.45 = 45/100. This back-and-forth conversion helps us understand that decimals and fractions are just two ways of writing the same value.
Comparing Decimals
To compare two decimal numbers, first compare their whole number parts. The number with the larger whole number part is greater. If the whole number parts are equal, compare the tenths digits. If those are also equal, compare the hundredths digits, and so on. For example, to compare 3.52 and 3.48: whole parts are both 3, so compare tenths: 5 > 4, so 3.52 > 3.48. It helps to write both numbers with the same number of decimal places by adding zeros at the end, like 3.5 = 3.50.
Adding and Subtracting Decimals
To add or subtract decimals, always line up the decimal points one below the other. Fill in any missing decimal places with zeros so both numbers have the same number of digits after the decimal point. Then add or subtract just like whole numbers, column by column from right to left, carrying or borrowing as needed. Place the decimal point in the answer directly below the decimal points in the question. For example, 2.35 + 1.4 becomes 2.35 + 1.40 = 3.75. This method keeps place values correctly aligned.
Key Concepts
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- 01A decimal number has two parts: the whole number part (left of the dot) and the decimal part (right of the dot).
- 02The first digit after the decimal point is in the tenths place, the second is in the hundredths place, and the third is in the thousandths place.
- 03Decimals can be compared by first comparing the whole number part, then the tenths digit, then the hundredths digit.
- 04Like fractions, decimals can be converted: 1/10 = 0.1, 1/100 = 0.01, 1/1000 = 0.001.
- 05Adding and subtracting decimals is done by aligning the decimal points and then computing column by column.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Write 8/100 as a decimal and name the place value of the digit 8 in your answer.
Compare 5.63 and 5.7. Which is greater?
Add 3.45 and 2.6.
Subtract 1.38 from 4.75.
Riya ran 2.350 km and Priya ran 2.305 km. Who ran more and by how much?
Decimals represent numbers between whole numbers using a decimal point. Digits to the right of the point are in tenths, hundredths, and thousandths places. Fractions with denominators 10, 100, or 1000 convert easily to decimals. We compare decimals place by place from left to right. Addition and subtraction of decimals require aligning the decimal points before calculating. Decimals are widely used in money, measurement, and daily life situations.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What is the place value of 4 in 7.04?
Q2.Which decimal is equal to 3/10?
Q3.What is 1.25 + 2.50?
Q4.Which of the following is the greatest?
Mark karo — dashboard par progress dikhega.