Identify the number of places the decimal must be moved in the dividend for the problem 166.4 ÷ 0.52. please
To solve the division problem 166.4 ÷ 0.52, we need to determine how many places the decimal must be moved in the dividend (166.4) in order to make the divisor (0.52) a whole number.
Since the divisor (0.52) has two decimal places, we would need to move the decimal in the dividend two places to the right to eliminate the decimals in the division problem.
2 spaces
thanks for the help!
To determine the number of places the decimal must be moved in the dividend for the problem 166.4 ÷ 0.52, we need to divide the dividend by the divisor and then count the decimal places in the quotient.
So let's perform the division:
166.4 ÷ 0.52
The dividend is 166.4, and the divisor is 0.52.
To make the divisor a whole number, we can multiply both the dividend and the divisor by 100. This allows us to move the decimal point two places to the right. Thus, the problem becomes:
166.4 × 100 ÷ (0.52 × 100)
= 16640 ÷ 52
Now we can perform the division:
319.9999999999999999999999808
__________________________
52 | 16640
To divide 16640 by 52, we start with the first digit of the dividend, which is 1. We divide 1 by 52 to get 0 as the first digit of the quotient.
0
________
52 | 16640
156
________
106
Then we bring down the next digit of the dividend, which is 6. The new partial dividend is now 106.
03
________
52 | 16640
156
________
106
104
________
200
We divide 106 by 52 to get 2 as the second digit of the quotient.
032
________
52 | 16640
156
________
106
104
________
200
156
________
440
Bringing down the last digit, 4, we find that it is not enough to divide by 52, so the quotient stops there.
Thus, the result is:
166.4 ÷ 0.52 = 319.9999999999999999999999808
So, to answer your question, the decimal must be moved 3 places to the right in the dividend for the problem 166.4 ÷ 0.52.
To determine the number of places the decimal must be moved in the dividend for the problem 166.4 ÷ 0.52, we need to consider the divisor, which is 0.52.
The divisor is a decimal, and when performing division, we usually convert the divisor into a whole number. To do that, we multiply both the dividend and the divisor by a power of 10 so that the divisor becomes a whole number.
In this case, the divisor is 0.52, which is equivalent to 52/100 or 13/25. To convert 0.52 into a whole number, we multiply both the dividend (166.4) and the divisor by 100.
166.4 * 100 = 16640 --- This is the new dividend
0.52 * 100 = 52 --- This is the new divisor
Now that the divisor is a whole number, we can perform long division to find the quotient. In doing so, we find that the quotient is 320.
Therefore, to answer your question, we moved the decimal point in the dividend 2 places to the right to convert the divisor into a whole number.