QuestionUngkapkan $3 \times 7^{4}+2 \times 7^{3}+5$ dalam bentuk nombor asas tujuh.

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3 \times7^{4}+ \times7^{3}+5$ . We need to express this number in base7

STEP 2

First, we need to calculate the value of the given expression.
$\times7^{4}+2 \times7^{}+5$

STEP 3

Calculate the value of $7^{}$ and $7^{3}$ .
$7^{} =2401$ $7^{3} =343$

STEP 4

Substitute the values of $7^{4}$ and $7^{3}$ into the expression.
$3 \times2401+2 \times343+$

STEP 5

Calculate the value of the expression.
$3 \times2401+2 \times343+5 =7203 +686 +5 =7894$

STEP 6

Now, we need to convert the decimal number7894 to base. We do this by repeatedly dividing by and keeping track of the remainders.

STEP 7

Divide7894 by7 and keep track of the remainder.
$7894 \div7 =1127 \, remainder \,5$

STEP 8

Divide the quotient from the previous step by7 and keep track of the remainder.
$1127 \div7 =161 \, remainder \,0$

STEP 9

Continue this process until the quotient is less than7.
$161 \div7 =23 \, remainder \,$ $23 \div7 =3 \, remainder \,2$ $3 \div7 = \, remainder \,3$

STEP 10

The number in base7 is the remainders read in reverse order.
$The \, number \, in \, base \,7 =32005$ The number $3 \times7^{4}+2 \times7^{3}+5$ in base7 is $32005_{7}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms