Multiplying by Powers of 10
Aligned to 5.NBT.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
A power of 10 like 10, 100, or 1,000 can be written with an exponent: 10 to the 1st, 2nd, or 3rd power. Multiplying by a power of 10 shifts the digits left (the number gets bigger); dividing shifts them right (smaller).
Worked examples
Example 1
Find 6.2 × 100. Since 100 is 10 to the 2nd power, the exponent is 2, so move the decimal point 2 places to the right: 6.2 becomes 620. Check with zeros: multiplying by 100 makes a number 100 times larger, and 6.2 × 100 = 620.
Example 2
Find 45 ÷ 10³. The exponent is 3, so move the decimal 3 places left: 45 becomes 0.045.
Example 3
10⁴ means 10 × 10 × 10 × 10 = 10,000 — the exponent counts the zeros, not the multiplications you do by hand.
Practice questions
- What is 45 × 1,000?
- What is 3.7 × 10 to the 2nd power?
- What is 500 ÷ 10 to the 2nd power?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Multiplicar por potencias de 10
Una potencia de 10 como 10, 100 o 1,000 se puede escribir con un exponente: 10 a la 1.ª, 2.ª o 3.ª potencia. Multiplicar por una potencia de 10 corre los dígitos a la izquierda (el número crece); dividir los corre a la derecha (se hace más pequeño).
Ejemplo 1: Halla 6.2 × 100. Como 100 es 10 a la 2.ª potencia, el exponente es 2, así que mueve el punto decimal 2 lugares a la derecha: 6.2 se convierte en 620. Comprueba con ceros: multiplicar por 100 hace el número 100 veces más grande, y 6.2 × 100 = 620.
Ejemplo 2: Halla 45 ÷ 10³. El exponente es 3, así que mueve el punto 3 lugares a la izquierda: 45 se vuelve 0.045.
Ejemplo 3: 10⁴ significa 10 × 10 × 10 × 10 = 10,000 — el exponente cuenta los ceros, no las multiplicaciones que haces a mano.
More Number & Operations in Base Ten lessons
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