Operations with Standard Form Flashcards

All 6 cards in this deck

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

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

1. Multiply the number parts: $3 \times 2 = 6$
2. Add the powers of $10$: $10^{5+4} = 10^{9}$
3. Check $1 \le A < 10$: $6 \times 10^{9}$

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 number parts: $8 \div 2 = 4$
2. Subtract the powers of $10$: $10^{7-3} = 10^{4}$
3. Check $1 \le A < 10$: $4 \times 10^{4}$

What must you do if your answer comes out as $18 \times 10^{-4}$?

Adjust it so $1 \le A < 10$: $1.8 \times 10^{-3}$.

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

e.g. $3 \times 10^{5} + 4 \times 10^{4}$

1. Write both as ordinary numbers: $300\,000$ and $40\,000$
2. Add them: $340\,000$
3. Write back in standard form: $3.4 \times 10^{5}$

True or false? To work out $2 \times 10^{3} + 3 \times 10^{3}$ you add the number parts and add the powers.

False. The powers stay the same when adding: the answer is $5 \times 10^{3}$.

True or false? A distance of $4 \times 10^{8}$ m is $100$ times greater than a distance of $4 \times 10^{6}$ m.

True. The power of $10$ is $2$ greater, so it is $10^2 = 100$ times bigger.