Can someone please solve this

Question

A person uses 400.8 kcal of energy to run a race. Convert the energy used for the race to the following energy units:

(provide an answer in 4 significant figures)

 Calories

 calories

 Food Calories

 Joules

 Kilojoules

Hint: 1kcal=4.184kJ

Answer 1

All we need to know to solve this problem is the conversion measurements for each of the energy units listed.

We are given that 1 kilocalorie is equal to 4.184 kilojoules

Our person ran a race and used 400.8 kilocalories.

We are asked to convert our 400.8 kilocalories into Calories, calories, food calories, joules, and kilojoules.

1. 400.8 kcal to Calories

"Calories" in this context, written with the capital C, is referring to food calories, which are actually measured in kilocalories. So,

400.8 kcal = 400.8 Calories

2.. 400.8 kcal to calories, lower-case c

Now we need to remember our metric unit conversions. A calorie is the base unit of a kilocalorie.

The mnemonic I was taught to memorize the order of metric units was

"King Henry Doesn't Usually Drink Chocolate Milk", K-H-D-U-D-C-M, kilo-hecto-deka-Unit(meters, liters, calories, etc)-deci-centi-milli, from biggest to smallest, with the basic unit in the center.

The unit is equal to one of itself. As you move to the left from U, you multiply by 10. As you move to the right, you divide by 10.

Therefore, in one kcal, there are 1000 calories.

400.8 kcal x 1000 calories = 400800 calories -to 4 sigfigs- 4.008 x 10⁵

1 kcal

3.. 400.8 kcal to food calories

As mentioned in number one, food calories, Calories, and kcal all refer to the same thing. The food we eat and how many Calories we burn is all actually measured in kcal. So;

400.8 kcal = 400.8 food calories

4.. 400.8 kcal to Joules

We are given the conversion factor that 1 kcal = 4.184 kJ

So, we will need to set up a table that first converts kcal to our given kJ, and then to Joules.

According to our metric conversions, we know that one kilojoule is equal to 1000 joules, the base unit.

400.8 kcal x 4.184 kJ x 1000 joules = 1676947.2 joules --to 4 sigfigs-- 1.677 x 10⁶ joules

1 kcal 1 kJ

5.. 400.8 kcal to KiloJoules

Now we can either divide our previous answer by 1000, as we know there are 1000 joules in one kilojoule, or we can rewrite our table without the conversion to joules:

400.8 kcal x 4.184 kJ = 1676.9472 kJ ;

1 kcal

to 4 significant figs, 1677 kJ