Find the tens digit of the integer.

01 / Standard#Your turn

103^{10}

Official paper · jm01-2021 · I.9 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Only the residue modulo 100 determines the last two digits.

Hint 2

Replace 103 by 3 modulo 100.

Worked solution

C: the tens digit is 4.

Checks and common pitfalls: The units digit 9 is not the requested tens digit.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Reduce the base before exponentiating.
$103^{10}\equiv3^{10}\pmod{100}$
Read the last two digits of the small power.
$3^{10}=59049\equiv49\pmod{100}$

Think first. Reveal a hint when the class is ready.

2021 JM01