An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Divide decimals by 10, 100, and 1000 by moving the decimal point to the left.
Perform long division to divide decimals.
Calculate average distance by dividing total distance by the number of litres: 176.96 ÷ 14 = 12.64 km/litre.
Calculate the number of ice cream cones: 10.5 × 1000 ÷ 75 = 140 cones.
Calculate the cost per showpiece: 230 ÷ 12 = 19.17 .
23.456 , 3.478 , 0.00056 ; 5.34057 , 1.34078 , 0.010356 ; 1.23456 , 0.384734 , 0.0020056 ; 45.63 , 2.034 , 1.0056 ; 100 , 336.95 , 0.08 ; 12.64 km / l i t re ; 140 co n es ; ₹19.17
Explanation
Problem Analysis We will solve the given decimal division problems, calculate the average distance traveled per liter of petrol, determine the number of ice cream cones that can be filled, and calculate the cost of a single showpiece.
Dividing by 10
(a) 234.56 ÷ 10 = 23.456 (b) 34.78 ÷ 10 = 3.478 (c) 0.0056 ÷ 10 = 0.00056
Dividing by 100
(a) 534.057 ÷ 100 = 5.34057 (b) 134.078 ÷ 100 = 1.34078 (c) 1.0356 ÷ 100 = 0.010356
Dividing by 1000
(a) 1234.56 ÷ 1000 = 1.23456 (b) 384.734 ÷ 1000 = 0.384734 (c) 2.0056 ÷ 1000 = 0.0020056
Long Division
(a) 547.56 ÷ 12 = 45.63 (b) 30.51 ÷ 15 = 2.034 (c) 14.0784 ÷ 14 = 1.0056
Decimal Division
(a) 4.56 ÷ 0.0456 = 100 (b) 134.78 ÷ 0.4 = 336.95 (c) 0.0056 ÷ 0.07 = 0.08
Average Distance
To find the average distance per litre, divide the total distance (176.96 km) by the number of litres (14 litres): a v er a g e _ d i s t an ce = 14 176.96 = 12.64 km/litre
Number of Ice Cream Cones
Convert 10.5 litres to millilitres: 10.5 × 1000 = 10500 ml. Then, divide the total volume of ice cream (10500 ml) by the volume per cone (75 ml): n u mb er _ o f _ co n es = 75 10500 = 140 cones
Cost per Showpiece
To find the cost of one showpiece, divide the total cost of a dozen showpieces ( ₹230 ) by 12: cos t _ p er _ s h o wp i ece = 12 230 = 19.166666666666668 ≈ 19.17
Final Answers The solutions to the problems are:
(a) 23.456, (b) 3.478, (c) 0.00056
(a) 5.34057, (b) 1.34078, (c) 0.010356
(a) 1.23456, (b) 0.384734, (c) 0.0020056
(a) 45.63, (b) 2.034, (c) 1.0056
(a) 100, (b) 336.95, (c) 0.08
12.64 km/litre
140 cones
₹ 19.17
Examples
Understanding decimal operations is crucial in everyday life. For instance, when calculating fuel efficiency, we divide the distance traveled by the amount of fuel consumed. Similarly, when distributing resources or calculating individual costs from a bulk purchase, we use division to ensure fair allocation and accurate budgeting. These mathematical skills empower us to make informed decisions and manage resources effectively.
