Dear Sue,
Thanks so much for helping me with exponents. Great help!
I have a new difficulty, metric conversion when it involves the prefixes. Some problems I need help with are:

1. 135 cg to hg
2. 0.537 eg to mg
3. 1.25 x 10 e5 nl to ml
4. 5.25 x 10 exp negative7 Gs to ds

 

Thanks again but I need this asap as usual. Patricia

Hi Patricia.

If you know how to work with exponents, you can work with any metric prefixes easily. Just remember that when multiplying 10a times 10b , the answer is 10a+b , but watch your signs. When you divide 10a over 10b , the answer is 10a-b .

Here is a list of all the metric prefixes that I know of and the exponents associated with each:

yotta- (Y-)

 1024 1 septillion

zetta- (Z-)

 1021 1 sextillion

exa- (E-)

 1018 1 quintillion

peta- (P-)

 1015 1 quadrillion

tera- (T-)

 1012 1 trillion

giga- (G-)

 109 1 billion

mega- (M-)

 106 1 million

kilo- (k-)

 103 1 thousand

hecto- (h-)

 102 1 hundred

deka- (da-)**

 10 1 ten

deci- (d-)

 10-1 1 tenth

centi- (c-)

 10-2 1 hundredth

milli- (m-)

 10-3 1 thousandth

micro- (µ-)

 10-6 1 millionth

nano- (n-)

 10-9 1 billionth

pico- (p-)

 10-12 1 trillionth

femto- (f-)

 10-15 1 quadrillionth

atto- (a-)

 10-18 1 quintillionth

zepto- (z-)

 10-21 1 sextillionth

yocto- (y-)

 10-24 1 septillionth

The way to work with this table is to convert the prefixes to exponents. I'll do this with your question #4, you do it for the others:

Question 4 asks us to convert 5.25 x 10-7 Gs to ds.

"Gs" is giga-seconds, that's 109 seconds. "ds" is deci-seconds, that's 10-1 seconds.
So

5.25 x 10-7 (x109) seconds
= 5.25 x (10-7 x 109) seconds
= 5.25 x 10-7+9 seconds
= 5.25 x 102 seconds.

Now convert to deci-seconds (ds). To do this, we divide instead of multiplying:

5.25 x 102 seconds
= 5.25 x 102 (/10-1) ds
= 5.25 x 102-(-1) ds
= 5.25 x 103 ds.

That's how it is done. Try this for the other questions.
Sue