Final answer:
Rounding and multiplying decimals involve moving the decimal point based on the power of 10 used. One eighth of 1,000 is 125, achieved by multiplying by the reciprocal of 8. When converting millimeters to meters, 1000 mm is equal to 1 m.
Step-by-step explanation:
When dealing with rounding and multiplying decimals, there are a few key concepts to keep in mind.
First, to find one eighth of 1,000, you can multiply by the reciprocal of 8, which is 0.125, yielding an answer of 125.
This makes sense as it's close to one tenth of 1,000 (which would be 100) but slightly larger.
When dividing or multiplying by powers of 10, we effectively move the decimal point.
For example, dividing 1.9436 by 1000 simply moves the decimal point three places to the left, resulting in 0.0019436.
Multiplying by powers of 10 moves the decimal to the right; thus, 2.4 multiplied by 100 becomes 240.
In terms of rounding, if we have a number like 1.9436 and we need to round it to the hundredth place, we would get 1.94 since the digit in the thousandth place is less than 5.
However, if we had a number like 921.996 and we need to round to the nearest hundredth, we look at the thousandth place, see that it's greater than 5, and hence round up to 922.00.
When converting millimeters to meters, the prefix milli- means 1/1000, so 1000 mm equals 1 m.
Lastly, to express a number in proper scientific form, you move the decimal point and use an exponent to keep track of the change.
For instance, 965 becomes 9.65 and we indicate that we moved the decimal point two places to the left by writing it as 9.65 × 10².