62
Multiplying a decimal fraction by a natural number
Textbook: Part 2, lesson 62, pp. 100–103
GoalMultiply a decimal by a natural number and by 10, 100, 1000.
New words
product · ko‘paytmamoving the point · vergulni surishfactor · ko‘paytuvchinumber of digits · raqamlar soni
Explanation
The product of a decimal and a natural number is the sum of addends each equal to the decimal, their number equal to the natural number. To calculate it, ignore the point and multiply the decimal as a natural number. In the product, separate from the right as many digits as there are digits after the point in the decimal. For example, 2.35 · 4: 235 · 4 = 940, separate two digits: 9.40 = 9.4. To multiply a decimal by 10, 100 or 1000, move the point 1, 2 or 3 places to the right; if digits run out, write zeros on the right: 4.95 · 1000 = 4950.
Worked examples
0.06 · 15: 6 · 15 = 90; there are 2 digits after the point, so 0.90 = 0.9.
3.47 · 100 = 347 (point 2 places right); 0.095 · 1000 = 95; 4.2 · 100 = 420 (one zero added).
Class activity
“Price cards”: write the prices of 4 products as decimals (for example, 1.5 thousand so‘m) and multiply to find the cost of 6 of each; check by repeated addition.
Practice
1
Calculate 3.14 · 5.
15.7
2
Calculate 0.25 · 40.
10
3
Calculate 7.205 · 100.
720.5
4
How many digits are separated in the product 1.25 · 6, and why?
Two — 1.25 has 2 digits after the point.