Use the prefix multipliers to express each measurement without...

Question

Use the prefix multipliers to express each measurement without any exponents.

a) 32 x 10^-13 L

b) 7.3 x 10⁶ g

c) 18.5 x 10¹¹ s

Accepted Answer

So here if we take a look at this practice question it says, use the prefix multipliers to express each measurement without any exponents. So this question is a combination of changing scientific notation to standard notation and also metric prefix conversions. Alright. So, basically, we're gonna have to change all these base units into some type of metric prefix and, in the process, get rid of these exponents. Alright. So for the first one, we have 32 times 10 to the negative 13 liters. If we think back to the metric prefix multipliers chart, we know that the only metric prefix that's close enough to 10 to the negative 13 is pico because pico is 10 to the negative 12. This means that we're gonna have to convert liters to pico liters. We have 32 times 10 to the negative 13 liters. I wanna get rid of liters, so I put liters on the bottom and pico liters on the top. Remember, the coefficient of 1 is associated or on the same side with the metric prefix, meaning 1 picot is 10 to the negative 12. Make sure you plug you put these in parentheses since there's times 10 to a power. Liters here cancel out. Now if you plug this correctly into your calculator, you should get back as your answer 3.2 pico liters. So we're able to change it to one of our prefix multipliers and in the process, we removed the exponent. So we've gone from scientific notation to, standard notation. For the next one, we have 10 to the 6. The metric prefix that's 10 to the 6 is mega. So here, we just have to convert grams to megagrams. We have 7.3 times 10 to the 6 grams. You wanna get rid of grams, so put them on the bottom, and we're converting to mega grams, so that goes on the top. The coefficient of 1 is on the same side with the metric prefix. So 1 mega is 10 to the negative oh, 10 to the positive 6. Make sure that these are in parenthesis, so when grams cancel out and you pluck this correctly in your calculator, you should get back 7.3 megagrams. And then finally, we have 18.5 times 10 to the 11 seconds. The metric prefix that's closest to 10 to the 11 is Tara because tera is 10 to 12. So we're gonna change seconds to teraseconds. So we have 18.5 times 10 to the 11 seconds, seconds go here on the bottom, and we're trying to find tera seconds, so they go on the top. One tera is 10 to 12th. Make sure this is in parenthesis. Seconds cancel out, and at the end, we'll have tera seconds as our answer. If you plug it in correctly, you'll get 1.85tera seconds as our final answer. So just remember, the question here was a little bit tricky, but read through it and realize they wanted you to change all these base units into metric prefixes, and in doing so, allow you to drop the exponent that's involved. So really, we're going from scientific notation to standard notation by incorporating the metric prefixes. Now that we've done this practice question, let's click on the next one and continue.

Struggling with Introduction to Chemistry?

Use the prefix multipliers to express each measurement without any exponents.
a) 32 x 10^-13 L
b) 7.3 x 10⁶ g
c) 18.5 x 10¹¹ s

Watch next

Metric Prefixes practice set

Struggling with Introduction to Chemistry?

Use the prefix multipliers to express each measurement without any exponents.a) 32 x 10-13 Lb) 7.3 x 106 g c) 18.5 x 1011 s

Watch next

Metric Prefixes practice set

Use the prefix multipliers to express each measurement without any exponents.
a) 32 x 10^-13 L
b) 7.3 x 10⁶ g
c) 18.5 x 10¹¹ s