Virginia SOL Math / Grade 7 / Number & Number Sense

7.NS.1

Powers of Ten & Scientific Notation

What you'll learn

  • Write numbers in scientific notation and back in standard form
  • Multiply and divide by powers of ten using patterns
  • Compare numbers written in scientific notation

Words to know

Scientific notation —
a number written as a value from 1 up to 10 times a power of ten
Power of ten —
10 raised to an exponent, such as 10 to the 3rd = 1,000
Exponent —
the small number that tells how many times to use the base as a factor
Coefficient —
the number from 1 up to 10 in scientific notation
Standard form —
a number written the usual way with all its digits

Why it matters Scientific notation lets us write and compare very large or very small numbers, like distances in space or the size of a cell, without long strings of zeros.

Worked examples

Model ItI do

Write 4,500,000 in scientific notation.

Move the decimal point left until one nonzero digit stays in front: 4.5. The point moved 6 places, so the power is 10 to the 6th. The answer is 4.5 times 10 to the 6th.

Try It TogetherWe do

Write 3.2 times 10 to the negative 4th in standard form.

A negative exponent means a small number, so move the decimal 4 places left: 0.00032. Count the places carefully to place each zero.

Now YouYou do

Write 78,000 in scientific notation.

Place one nonzero digit before the decimal and count how many places it moved. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Write 10^3 as a standard number.

  2. 2.Write 500 in scientific notation.

  3. 3.Write 6 x 10^4 in standard form.

On Level

The core Quick Check from the book.

  1. 1.Write 6,300,000 in scientific notation.

  2. 2.Write 2.5 times 10 to the 5th in standard form.

  3. 3.Write 0.00047 in scientific notation.

  4. 4.Which is larger: 3 times 10 to the 4th or 8 times 10 to the 3rd?

  5. 5.Find 10 to the 3rd times 10 to the 2nd as a single power of ten.

Challenge

Stretch your thinking.

  1. 1.Write 0.00082 in scientific notation.

  2. 2.Which is larger: 4.5 x 10^6 or 9 x 10^5? Explain in one phrase.

  3. 3.Find 10^4 x 10^3 written as a single power of ten.