We read numbers like 0.1, 0.2, 0.3 … as ‘zero point one’, ‘zero point two’, ‘zero point three’ and so on. Zero is written to indicate the place of the whole number. A decimal number has two parts. 48 . 35 Whole or integral part Decimal part (= or > 0) (< 1) Decimal Point Note: T he numbers in the decimal part are read as separate digits. Recall the place value chart of numbers. 100 × 10 10 × 10 1 × 10 1 Thousands Hundreds Tens Ones 6 2 5 5 3 2 2 6 5 2 We know that in this chart, as we move from right to left, the value of the digit increases 10 1 times. Also, as we move from left to right, the value of a digit becomes times. The place 10 value of the digit becomes one-tenth, read as a tenth. Its value is 0.1 read as ‘zero point one’. 2 is read as ‘two-tenths’, 7 is read as ‘seven–tenths’ and so on. 10 10 We can extend the place value chart to the right as follows: 1 × 1000 1 × 100 1 × 10 1 . 1 10 Thousands Hundreds Tens Ones Decimal Tenths 7 . 2 1 2 4 . 3 30 4 3 . 6 1 5 . 7 The number 3015.7 is read as three thousand and fifteen point seven. Similarly, the other numbers are read as follows: 3 1/7/2019 3:00:20 PM NR_BGM_9789386663368 MAPLE G04 INTEGRATED TEXTBOOK TERM 3_Text.pdf 44
Seven point two; twenty-four point three and one hundred and forty-three point six. The point placed in between the number is called the decimal point. The system of writing numbers using a decimal point is called the decimal system. [Note: ‘Deci’ means 10.] Hundredths: Study this place value chart. Thousands Hundreds Tens Ones Decimal Tenths Hundredths 1 × 10 1 point 1 × 1000 1 × 100 2 1 1 2 8 6 . 10 100 3 . 9 When the number moves right from the tenths place, we get a new place, which is 1 of the tenths place. It is called the ‘hundredths’ place written as 1 and read 10 100 as one-hundredths. Its value is 0.01, read as ‘zero point zero one’. 2 is read as two-hundredths, 5 is read as five-hundredths and so on. 100 100 So, the number in the place value chart is read as ‘two thousand eight hundred and sixty-two point three nine’. Expansion of decimal numbers Using the place value chart, we can expand decimal numbers. Let us see a few examples. Example 1: Expand these decimals. a) 1430.8 b) 359.65 c) 90045.75 d) 654.08 Solution: To expand the given decimal numbers, first write them in the place value chart as shown. S. no Ten Thousands Hundreds Tens Ones Decimal Tenths Hundredths thousands 1 point a) 4 3 0 . 8 b) 9 0 3 5 9 65 c) 0 4 5 . 75 d) 6 5 4 08 . . Decimals 4 NR_BGM_9789386663368 MAPLE G04 INTEGRATED TEXTBOOK TERM 3_Text.pdf 45 1/7/2019 3:00:20 PM
Expansions: 1 a) 1430.8 = 1 × 1000 + 4 × 100 + 3 × 10 + 0 × 1 + 8 × 10 b) 359.65 = 3 × 100 + 5 × 10 + 9 × 1 + 6 × 1 + 5 × 1 Example 2: 10 100 c) 90045.75 = 9 × 10000 + 0 × 1000 + 0 × 100 + 4 × 10 + 5 × 1 + 7 × 1 + 5 × 1 10 100 1 1 d) 654.08 = 6 × 100 + 5 × 10 + 4 × 1 + 0 × + 8 × Solution: 10 100 Write these as decimals. a) 7 × 1000 + 2 × 100 + 6 × 10 + 3 × 1 + 9 × 1 + 3 × 1 10 100 b) 3 × 10000 + 0 × 1000 + 1 × 100 + 9 × 10 + 6 × 1 + 4 × 1 + 5 × 1 10 100 c) 2 × 1000 + 2 × 100 + 2 × 10 + 2 × 1 + 2 × 1 + 2 × 1 10 100 d) 5 × 100 + 0 × 10 + 0 × 1 + 0 × 1 + 5 × 1 10 100 First write the numbers in the place value chart as shown. S. no Ten Thousands Hundreds Tens Ones Decimal Tenths Hundredths thousands point a) 7 2 63 . 93 b) 3 0 1 96 . 45 c) 2 2 22 . 22 d) 5 00 . 05 Standard forms of the given decimals are: a) 7263.93 b) 30196.45 c) 2222.22 d) 500.05 Conversion of fractions to decimals Fractions can be written as decimals. Consider an example. Example 3: Express these fractions as decimals. a) 18 2 b) 43 5 c) 26 1 d) 4 9 10 10 10 10 Solution: To write the given fractions as decimals, follow these steps. Step 1: Write the integral part as it is. Step 2: Place a point to its right. 5 1/7/2019 3:00:20 PM NR_BGM_9789386663368 MAPLE G04 INTEGRATED TEXTBOOK TERM 3_Text.pdf 46
Step 3: Write the numerator of the proper fraction part. a) 18 2 = 18.2 b) 43 5 = 43.5 10 10 c) 26 1 = 26.1 d) 4 9 = 4.9 10 10 Example 4: Express these fractions as decimals. a) 25 b) 17 2 c) 43 d) 5 92 100 100 100 100 Solution: a) 25 = 25 hundredths = 0.25 100 b) 17 2 = 17 and 2 hundredths = 17.02 100 c) 43 = 43 hundredths = 0.43 100 d) 5 92 = 5 and 92 hundredths = 5.92 100 Shortcut method: Fractions having 10 or 100 as their denominators, can be expressed in their decimal form by following the steps given below. Step 1: Write the numerator. Step 2: Then count the number of zeros in the denominator. Step 3: Place the decimal point after the same number of digits from the right as the number of zeros. For example, the decimal form of 232 = 2.32 100 Note: F or the decimal equivalent of a proper fraction, place a 0 as the integral part of the decimal number. Conversion of decimals to fractions To convert a decimal into a fraction, follow these steps. Step 1: Write the number without the decimal. Step 2: Count the number of decimal places (that is, the number of places to the right of the decimal number). Step 3: Write the denominator with 1 followed by as many zeros as the decimal point. Decimals 6 NR_BGM_9789386663368 MAPLE G04 INTEGRATED TEXTBOOK TERM 3_Text.pdf 47 1/7/2019 3:00:20 PM
Example 5: Write these decimals as fractions. a) 2.3 b) 13.07 c) 105.43 d) 0.52 Solution: a) 2.3 = 23 b) 13.07 = 1307 10 100 c) Alternate method: 105.43 = 10543 d) 0.52 = 52 100 100 A decimal having an integral part can be written as a mixed fraction. So, 2.3 = 2 and 3 tenths = 2 3 10 13.07 = 13 and 7 hundredths = 13 7 100 105.43 = 105 and 43 hundredths = 105 43 100 7 1/7/2019 3:00:20 PM NR_BGM_9789386663368 MAPLE G04 INTEGRATED TEXTBOOK TERM 3_Text.pdf 48
Search
