To estimate the division [tex]\(1546 \div 37\)[/tex] by first rounding each number to have only one nonzero digit, follow these steps:
1. Round the Dividend:
The original dividend is 1546. We need to round this number so that it has only one nonzero digit. Looking at the nearest values, we can round 1546 down to the nearest value with one significant nonzero digit, which is 1500.
2. Round the Divisor:
The original divisor is 37. Similarly, we need to round this value to have only one nonzero digit. The nearest value to 37 that fits this criterion is 40.
3. Perform the Division:
Now we will use the rounded numbers to estimate the division:
[tex]\[
\frac{1500}{40}
\][/tex]
4. Calculate the Estimated Result:
To find the result of [tex]\(\frac{1500}{40}\)[/tex], we perform the calculation:
[tex]\[
\frac{1500}{40} = 37.5
\][/tex]
So, the estimated result of [tex]\(1546 \div 37\)[/tex], after rounding each number to have only one nonzero digit, is 37.5.
