How many zeros are at the end of 458 · 885? Explain how you can answer this question without actually computing the number. (Hint: 10 = 2 · 5.) When this number is written in ordinary decimal form, each 0 at its end comes from a factor of , or one factor of 2 and one factor of . g

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Answer:

One zero

Step-by-step explanation:

To find : number of zeroes at the end of product 458 · 885 .

It's given that when this number is written in ordinary decimal form, each 0 at its end comes from a factor of , or one factor of 2 and one factor of . g

First, we will find factors of 458 and 885 .

[tex]458=2\times 229\\885=3\times 5\times 59[/tex]

From this factorisation, we get

[tex]458\cdot 885=2\times 229\times 3\times 5\times 59[/tex]

i,e, [tex]458\cdot 885=2\times 3\times 5\times 59\times 229[/tex]

Here, we noticed that we have one 2 and one 5, which makes [tex]2\times 5=10[/tex]

So, we conclude that 458 · 885 ends at one zero .

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