If the volume of a Box is 1,463,000 cubic millimetres, what is the vol

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\(Well,\; square\; meters\; or\; cubic\; meters\; are\; simply\; m*m,\)

\(so\; our\; nice\; "a\; lot\; of\; millions"mm^{3},\; means\; x_{mm}\cdot y_{mm}\cdot z_{mm}\; and\; as\; each\; of\; these\; mm\; has\; a\; conversion\; of\; \frac{1}{1000},\)

\(the\; whole\; pack\; will\; need\; a\; reduction\; of\; 10^{-9}\; ,\; 9\; zeros,\; to\; become\; m^{3}.\)

\(Answer\; \mbox{E}.\)

\(Hope\; it\; helps.\;\) \(:)\)

Den

Comma's should be converted to points for better understanding of the problem .

Hi pushpitkc

i dont get for some reason logic of sentence in red...

if 1 mm is 0.001 cubic mt. then

then shouldnt we divide 1463000 by 0,001

Hi dave13

1 mm is 0.001 mt
1 cubic mm will be \((0.001)^3 = 0.000000001\) cubic meter

Since we are given the volume of the box is 1,463,000 cubic millimeters, to convert into
cubic meter, we need to multiply it by 0.000000001.
1,463,000 cubic mm = 1,463,000*0.000000001 = 0.01463 cubic meter.

Hope this helps you!

We know that when you multiply numbers with decimals, you multiply the numbers and then shift the decimal point to the left as many times as there are spaces to the right of the decimals in both numbers.

We are given that 1 millimeter = 0.001 meter

1 cubic meter= (.001)(.001)(.001) cubic millimeters

It follows that 1 cubic millimeter = 1 cubic meter (followed by 9 decimal shifts to the left).

How do we get from cubic millimeters to cubic meters? We shift the decimal 9 spaces to the left.

We can see that 7 shift gets us .1463000 so 9 shifts gets us .001463000 cubic meters

don't we need to convert twice such as 1463000 cubic millimeters to millimeters and 0.001 meter to cubic meters?
I mean we only convert the later one. Give me a more thorough solution. Bunuel

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Hi Matt,

How're you getting the number highlighted above? I'm quite confused as to how you come arrive at this number and why.

Multiplying decimals can be tricky — I'll quickly walk you guys through how to get the right number with decimal multiplication, and then I'll tell you what (I think) is an easier way to handle this type of math.

As established, for every cubic mm, we have (0.001)^3 cubic m, or 0.001 * 0.001 * 0.001. When we multiply decimals, we first want to multiply the numbers as if the decimal didn't exist. So 0001 * 0001 * 0001 = 1. Then, we want to add up how many places there were in total to the right of the decimal in the numbers we multiplied together. Each 0.001 has three places to the right of the decimal, so there are nine places to the right of the decimal in total. We then apply this to the answer we got when we ignored the decimal. So taking 1 (where the decimal is after the one) and moving the decimal nine places to the left gives us 0.000000001.

A different approach is to turn everything into scientific notation — this allows us to use our exponent rules. So 0.001^3 becomes (10^-3)^3, which equals 10^-9 or 0.000000001.

In general, exponents are easier than decimals, so I recommend the scientific notation approach. While some problems are most easily solved with decimals, you'll often see that finding another way to express the numbers (exponents, fractions, etc.) will make your life easier.

Since we are going from \(mm^{3}\) to \(m^{3}\), we have to multiply by the ratio of meters to millimeters until the millimeter-unit is gone, and it has been replaced with the cubed meter-unit:

1,463,000 \(mm^{3}\) * \(\frac{1m}{1000mm}\) * \(\frac{1m}{1000mm}\) * \(\frac{1m}{1000mm}\)= 0.001463 \(m^{3}\)

It's easy as 1,2,3

\(1463000*\frac{1}{1000^3}=0.001463\), Answer must be (E)