Operations with Standard form Flashcards

All 7 cards in this deck

What are the steps to multiply two numbers in standard form?

e.g. $(3 \times 10^{5}) \times (4 \times 10^{-2})$

1. Multiply the front numbers: $3 \times 4 = 12$
2. Add the powers of 10: $10^{5+(-2)} = 10^{3}$
3. Rewrite in standard form: $12 \times 10^{3} = 1.2 \times 10^{4}$

What are the steps to divide two numbers in standard form?

e.g. $(8 \times 10^{7}) \div (2 \times 10^{3})$

1. Divide the front numbers: $8 \div 2 = 4$
2. Subtract the powers of 10: $10^{7-3} = 10^{4}$
3. Check $A$ is between 1 and 10: $4 \times 10^{4}$

What are the steps to add two numbers in standard form?

e.g. $9.7 \times 10^{6} + 2.45 \times 10^{7}$

1. Write both with the same power of 10: $9.7 \times 10^{6} + 24.5 \times 10^{6}$
2. Add the front numbers: $34.2 \times 10^{6}$
3. Write in standard form: $3.42 \times 10^{7}$

True or false? $(3 \times 10^{5}) + (4 \times 10^{5}) = 7 \times 10^{10}$.

False. When adding like this the power of 10 stays the same: $7 \times 10^{5}$.

How do you work out how many times bigger one number in standard form is than another?

e.g. $4.35 \times 10^{9}$ compared with $4.14 \times 10^{7}$

Divide the larger by the smaller: $(4.35 \times 10^{9}) \div (4.14 \times 10^{7}) = 105$ (to the nearest whole number), so it is over 100 times bigger.

What are the steps to find the average mass of one item when the total mass and the number of items are given in standard form?
e.g. $2 \times 10^{12}$ cells have a total mass of $90$ g

1. Divide the total mass by the number of items: $90 \div (2 \times 10^{12}) = 45 \times 10^{-12}$
2. Rewrite in standard form: $4.5 \times 10^{-11}$ g

True or false? A calculator display of $4.52\text{E}7$ means $4.52 \times 10^{7}$.

True. The E (or $\times 10^{x}$ output) gives the power of 10, so it should be written as $4.52 \times 10^{7}$.